Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class CF1016_E {
    public static void main(String[] args)throws Throwable {
        MyScanner sc=new MyScanner();
        PrintWriter pw=new PrintWriter(System.out);

        int ys=sc.nextInt();
        int a=sc.nextInt();
        int b=sc.nextInt();
        int n=sc.nextInt();
        int [] l=new int [n];
        int [] r=new int [n];
        for(int i=0;i<n;i++){
            l[i]=sc.nextInt();
            r[i]=sc.nextInt();
        }
        long [] cum=new long [n];
        cum[0]=r[0]-l[0];
        for(int i=1;i<n;i++)
            cum[i]=cum[i-1]+r[i]-l[i];
        double all=b-a;
        int q=sc.nextInt();
        while(q-->0){
            int xp=sc.nextInt();
            int yp=sc.nextInt();
            double x1=(-1.0*ys*(xp-a))/(yp-ys)+a;
            double x2=(-1.0*ys*(xp-b))/(yp-ys)+b;
            double ratio=0;
            int start=0,end=n-1,leftComp=n;
            while(start<=end){
                int mid=(start+end)/2;
                if(l[mid]>x1-eps){
                    leftComp=mid;
                    end=mid-1;
                }else
                    start=mid+1;
            }
            start=0;end=n-1;
            int rightComp=-1;
            while(start<=end){
                int mid=(start+end)/2;
                if(r[mid]<x2+eps){
                    rightComp=mid;
                    start=mid+1;
                }else
                    end=mid-1;
            }
            if(leftComp!=n && rightComp!=-1 && leftComp<=rightComp){
                ratio+=cum[rightComp];
                if(leftComp>0)
                    ratio-=cum[leftComp-1];
            }
            rightComp++;
            leftComp--;
            if(rightComp==leftComp)
                ratio=x2-x1;
            else{
                if(leftComp>=0 && leftComp<n){
                    double tmp=Math.max(0,r[leftComp]-x1);
                    ratio+=tmp;
                }
                if(rightComp>=0 && rightComp<n){
                    double tmp=Math.max(0,x2-l[rightComp]);
                    ratio+=tmp;
                }
            }

            ratio/=(x2-x1);
            pw.println(ratio*all);
        }

        pw.flush();
        pw.close();
    }

    static double eps=1e-9;

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {while (st == null || !st.hasMoreElements()) {
            try {st = new StringTokenizer(br.readLine());}
            catch (IOException e) {e.printStackTrace();}}
            return st.nextToken();}
        int nextInt() {return Integer.parseInt(next());}
        long nextLong() {return Long.parseLong(next());}
        double nextDouble() {return Double.parseDouble(next());}
        String nextLine(){String str = "";
            try {str = br.readLine();}
            catch (IOException e) {e.printStackTrace();}
            return str;}
    }
}